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3.2 Algebra and Functions (A-level only)

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Question 25

The signal strength SSS, measured in decibels (dB), of a satellite passing directly over a ground station is modeled by the function

S(t)=24−4∣5−t∣,t≥0 S(t) = 24 - 4|5 - t|, \quad t \ge 0 S(t)=24−4∣5−t∣,t≥0

where t t\,t is the time in minutes since the signal was first detected.

a.

Find the value of SS(8)SS(8)SS(8).

[2]
b.

Solve the equation S(t)=2tS(t) = 2tS(t)=2t.

[4]
c.

Given that the equation S(t)=kS(t) = kS(t)=k has exactly two distinct solutions for ttt, determine the range of possible values for the constant kkk.

[2]
d.

A calibration adjustment transforms the signal graph into the graph with equation y=pS(t−q)y = pS(t - q)y=pS(t−q). The vertex of this transformed graph is at (1,12)(1, 12)(1,12). Find the value of the constants p p\,p and qqq.

[3]
Markscheme

3.2 Algebra and Functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.2 Algebra and Functions (A-level only)

216 exam-style questions on WJEC A Level Maths 3.2 Algebra and Functions (A-level only), covering 3.2.1 Algebra and Functions (A-level only), 3.2.2 Algebra and Functions (A-level only), 3.2.3 Algebra and Functions (A-level only), 3.2.4 Algebra and Functions (A-level only), 3.2.5 Algebra and Functions (A-level only), 3.2.6 Algebra and Functions (A-level only), and 3.2 Algebra and Functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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